The instability of chaotic synchronization in coupled Lorenz systems: from the Hopf to the Co-dimension two bifurcation

We investigate the Hopf bifurcation of the synchronous chaos in coupled Lorenz oscillators. We find that the system undergoes a phase transition along the Hopf instability of the synchronous chaos. The phase transition makes the traveling wave component with the phase difference φ(i)-φ(i+1)=2π/N between adjacent sites unstable. The phase transition also plays a role to relate the Hopf bifurcation with the co-dimension two bifurcation of the synchronous chaos. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005